The US Coast Guard has a rather different remit to the RNLI which is devoted purely to rescue. I believe the USCG has other duties as well. Contrast: https://www.uscg.mil/ and https://rnli.org/
The UK and Eire have a huge coastline relative to their land area and the RNLI are a treasured institution. Mostly staffed by volunteers and financed as a charity. We also have a Coast Guard which is actually responsible for search and rescue at sea. It's a little bit complicated but you will be pulled out of the water by a very highly trained civilian volunteer.
There is no reason not to start a non military ANLI. The RNLI already have boat designs that are proven and a operational model that is also proven. Just copy it.
You (US) have made your choice on how you want to be rescued at sea and we have made ours. They are simply different models on how to do it.
Once the RNLI was founded as a charity there was of course no pragmatic reason to dedicate tax money to that mission, so here we are today. The contracted Coast Guard helicopter pilots on £150k each hovering beside a lifeboat staffed by volunteers. Whilst the paid RNLI executives sleep.
Something's not right there and that's not a model I'd encourage others to adopt. If maritime rescue is considered worthwhile then it should be professionally rewarded, and at all levels.